1. On Wolff's L5/2-Kakeya maximal inequality in R³.
- Author
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Changxing Miao, Jianwei Yang, and Jiqiang Zheng
- Subjects
- *
MATHEMATICAL inequalities , *DIFFERENTIAL equations , *MATHEMATICAL proofs , *MATHEMATICAL bounds , *SET theory - Abstract
We reprove Wolff's L5/2-bound for the R³-Kakeya maximal function without appealing to the argument of induction on scales. The main ingredient in our proof is an adaptation of Sogge's strategy used in the work on Nikodym-type sets in curved spaces. Although the equivalence between these two type maximal functions is well known, our proof may shed light on some new geometric observations which is interesting in its own right. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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